Solve the problem by using a nonlinear system.
-In 1982, City $\# 1$ and City $\# 2$ had the same population. The population of City $\# 2$ continued to increase steadily, while the rate of population growth of City $\# 1$ (although initially less than that of City \#2) eventually overtook the growth rate of City \#2. The populations of two cities are modeled by the following equations: City $\# 1: y=2 x^{2}+15 x+1192$; City $\# 2: y=25 x+1192$, where $x=0$ corresponds to the year 1982. In what year after 1982 did the cities have the same population?
A) 1987
B) 1988
C) 1986
D) 1985

Question

Quizplus · Accepted Answer

To find when the populations are equal, set the equations equal: $2x^2 + 15x + 1192 = 25x + 1192$. Simplifying gives $2x^2 - 10x = 0$, or $2x(x - 5) = 0$. Thus, $x = 0$ or $x = 5$. Since $x = 0$ corresponds to 1982, $x = 5$ corresponds to 1987.

Solve the Problem by Using a Nonlinear System #1\# 1#1 And City

Solve the Problem by Using a Nonlinear System $\# 1$ And City